New probe of non-Gaussianities with primordial black hole induced gravitational waves

We propose a new probe of primordial non-Gaussianities (NGs) through the observation of gravitational waves (GWs) induced by ultra-light (M₏₁₇< 10^9g) primordial black holes (PBHs). Interestingly enough, the existence of primordial NG can leave imprints on the clustering properties of PBHs and the spectral shape of induced GW signals. Focusing on a scale-dependent local-type NG, we identify a distinct double-peaked GW energy spectrum that, contingent upon M₏₁₇ and the abundance of PBHs at the time of formation, denoted as PBH, f, may fall into the frequency bands of upcoming GW observatories, including LISA, ET, SKA, and BBO. Thus, such a signal can serve as a novel portal for probing primordial NGs. Intriguingly, combining BBN bounds on the GW amplitude, we find for the first time the joint limit on the product of the effective non-linearity parameter for the primordial tri-spectrum, denoted by NL, and the primordial curvature perturbation power spectrum P ₑ (k), which reads as NL P ₑ (k) < 4 10^-20 ^-17/9PBH, f (M ₏₁₇10⁴g) ^-17/9.